List of spirals
This list is incomplete; you can help by adding missing items. (February 2019) |
This list of spirals includes named spirals that have been described mathematically.
Image | Name | First described | Equation | Comment | |
---|---|---|---|---|---|
![]() | circle | The trivial spiral | |||
![]() | Archimedean spiral (also arithmetic spiral) | c. 320 BC | |||
![]() | Fermat's spiral (also parabolic spiral) | 1636[1] | |||
![]() | Euler spiral (also Cornu spiral or polynomial spiral) | 1696[2] | using Fresnel integrals[3] | ||
![]() | hyperbolic spiral (also reciprocal spiral) | 1704 | |||
![]() | lituus | 1722 | |||
![]() | logarithmic spiral (also known as equiangular spiral) | 1638[4] | Approximations of this are found in nature | ||
![]() | Fibonacci spiral | circular arcs connecting the opposite corners of squares in the Fibonacci tiling | approximation of the golden spiral | ||
![]() | golden spiral | special case of the logarithmic spiral | |||
![]() | Spiral of Theodorus (also known as Pythagorean spiral) | c. 500 BC | contiguous right triangles composed of one leg with unit length and the other leg being the hypotenuse of the prior triangle | approximates the Archimedean spiral | |
![]() | involute | 1673 |
| involutes of a circle appear like Archimedean spirals | |
![]() | helix | a 3-dimensional spiral | |||
![]() | Rhumb line (also loxodrome) | type of spiral drawn on a sphere | |||
![]() | Cotes's spiral | 1722 | Solution to the two-body problem for an inverse-cube central force | ||
![]() | Poinsot's spirals | ||||
![]() | Nielsen's spiral | 1993[5] | A variation of Euler spiral, using sine integral and cosine integrals | ||
![]() | Polygonal spiral | special case approximation of arithmetic or logarithmic spiral | |||
![]() | Fraser's Spiral | 1908 | Optical illusion based on spirals | ||
![]() | Conchospiral | three-dimensional spiral on the surface of a cone. | |||
![]() | Calkin–Wilf spiral | ||||
![]() | Ulam spiral (also prime spiral) | 1963 | |||
![]() | Sack's spiral | 1994 | variant of Ulam spiral and Archimedean spiral. | ||
Seiffert's spiral | 2000[6] | spiral curve on the surface of a sphere using the Jacobi elliptic functions[7] | |||
![]() | Tractrix spiral | 1704[8] | |||
Pappus spiral | 1779 | 3D conical spiral studied by Pappus and Pascal[9] | |||
![]() | doppler spiral | 2D projection of Pappus spiral[10] | |||
![]() | Atzema spiral | The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral.[11] | |||
![]() | Atomic spiral | 2002 | This spiral has two asymptotes; one is the circle of radius 1 and the other is the line [12] | ||
![]() | Galactic spiral | 2019 | The differential spiral equations were developed to simulate the spiral arms of disc galaxies, have 4 solutions with three different cases:, the spiral patterns are decided by the behavior of the parameter . For , spiral-ring pattern; regular spiral; loose spiral. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by () for plotting.[13][predatory publisher] |
See also
- Catherine wheel (firework)
- List of spiral galaxies
- Parker spiral
- Spirangle
- Spirograph
References
- ^ "Fermat spiral - Encyclopedia of Mathematics". www.encyclopediaofmath.org. Retrieved 18 February 2019.
- ^ Weisstein, Eric W. "Cornu Spiral". mathworld.wolfram.com. Retrieved 2023-11-22.
- ^ Weisstein, Eric W. "Fresnel Integrals". mathworld.wolfram.com. Retrieved 2023-01-31.
- ^ Weisstein, Eric W. "Logarithmic Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
- ^ Weisstein, Eric W. "Nielsen's Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
- ^ Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com. Retrieved 2023-01-31.
- ^ Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com. Retrieved 2023-01-31.
- ^ "Tractrix spiral". www.mathcurve.com. Retrieved 2019-02-23.
- ^ "Conical spiral of Pappus". www.mathcurve.com. Retrieved 28 February 2019.
- ^ "Doppler spiral". www.mathcurve.com. Retrieved 28 February 2019.
- ^ "Atzema spiral". www.2dcurves.com. Retrieved 11 March 2019.
- ^ "atom-spiral". www.2dcurves.com. Retrieved 11 March 2019.
- ^ Pan, Hongjun. "New spiral" (PDF). www.arpgweb.com. Retrieved 5 March 2021.
- v
- t
- e
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/59/Golden_spiral_in_triangles.png/60px-Golden_spiral_in_triangles.png)
Biochemistry |
---|